先化简,再求值:(a-1)/a ÷ {a -(2a-1)/a},其中a=√3+1
问题描述:
先化简,再求值:(a-1)/a ÷ {a -(2a-1)/a},其中a=√3+1
先化简,再求值:(a-1)/a ÷ {a -(2a-1)/a},其中a=√3+1
答
[(a-1)/a]÷[a-(2a-1)/a]
=[(a-1)/a]÷[(a²-2a+1)/a]
=[(a-1)/a]÷[(a-1)²/a]
=[(a-1)/a]×[a/(a-1)²]
=1/(a-1)
所以,当a=√3+1时,原式=1/[(√3+1)-1]=1/√3=√3/3